This is very much possible. First , You will have to restructure your View Hierarchy as below.

Then transform your Design BOM to Mfg using the New Downstream part action as mentioned by you. This will be your Master or Plant Neutral BOM. From manufacturing you can then transform to Plant1, 2 and so on using the New Downstream Branch action instead of new downstream part. This way you will have the same number for the part to be used in multiple plants and subsequent push to ERP.
I would recommend you do a thorough testing with this setup. NOTE that the view hierarchy changes will NOT be possible once transformations are carried out based on a particularly view hierarchy. So plan the View hierarchy upfront. Spend as much time possible to brainstorm with multiple stakeholders before finalizing anything putting in Production.
Hope this helps.
Regards
~Syed